Least Common Multiple (LCM) of 113 and 154
The least common multiple (LCM) of 113 and 154 is 17402.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 113 and 154?
First, calculate the GCD of 113 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 154 = 0 remainder 113 |
| 2 | 154 ÷ 113 = 1 remainder 41 |
| 3 | 113 ÷ 41 = 2 remainder 31 |
| 4 | 41 ÷ 31 = 1 remainder 10 |
| 5 | 31 ÷ 10 = 3 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 63 and 189 | 189 |
| 194 and 52 | 5044 |
| 106 and 175 | 18550 |
| 135 and 105 | 945 |
| 59 and 148 | 8732 |